4x^2-19x-15=0

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Solution for 4x^2-19x-15=0 equation: 


Simplifying
4x2 + -19x + -15 = 0

Reorder the terms:
-15 + -19x + 4x2 = 0

Solving
-15 + -19x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-3.75 + -4.75x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -4.75x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -4.75x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -4.75x + x2 = 0 + 3.75
-4.75x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-4.75x + x2 = 3.75

The x term is -4.75x.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75x + 5.640625 + x2 = 3.75 + 5.640625

Reorder the terms:
5.640625 + -4.75x + x2 = 3.75 + 5.640625

Combine like terms: 3.75 + 5.640625 = 9.390625
5.640625 + -4.75x + x2 = 9.390625

Factor a perfect square on the left side:
(x + -2.375)(x + -2.375) = 9.390625

Calculate the square root of the right side: 3.064412668

Break this problem into two subproblems by setting 
(x + -2.375) equal to 3.064412668 and -3.064412668.


Subproblem 1
x + -2.375 = 3.064412668

Simplifying
x + -2.375 = 3.064412668

Reorder the terms:
-2.375 + x = 3.064412668

Solving
-2.375 + x = 3.064412668

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.375' to each side of the equation.
-2.375 + 2.375 + x = 3.064412668 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + x = 3.064412668 + 2.375
x = 3.064412668 + 2.375

Combine like terms: 3.064412668 + 2.375 = 5.439412668
x = 5.439412668

Simplifying
x = 5.439412668


Subproblem 2
x + -2.375 = -3.064412668

Simplifying
x + -2.375 = -3.064412668

Reorder the terms:
-2.375 + x = -3.064412668

Solving
-2.375 + x = -3.064412668

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.375' to each side of the equation.
-2.375 + 2.375 + x = -3.064412668 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + x = -3.064412668 + 2.375
x = -3.064412668 + 2.375

Combine like terms: -3.064412668 + 2.375 = -0.689412668
x = -0.689412668

Simplifying
x = -0.689412668


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.439412668, -0.689412668}

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